RDP 2015-10: The Life of Australian Banknotes 7. Back-testing the Models
August 2015 – ISSN 1448-5109 (Online)
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A number of currency issuers sample banknotes as a means of examining the quality of banknotes in circulation. In the case of Australia, the RBA examines samples of unfit banknotes ready for destruction and also samples from the general population of banknotes in circulation. Aside from their primary purpose (to study banknote quality), the samples can also be used as an empirical test of the results from the survival models and provide some interesting details about the age distribution of banknotes.
7.1 Sampling Unfit Banknotes
The survival models can be used to predict the median age of banknotes that become unfit at a point in time, using data and estimates for the production vintage of banknotes issued at each point in time.[15] In Australia, unfit banknotes are returned to the National Note Processing and Distribution Centre (NNPDC), where they are validated, assessed and destroyed. A sample of around 800,000 unfit banknotes was extracted in 2011 and sorted into production vintages.[16] These data were then compared to the composition of unfit banknotes predicted by the survival models and the traditional steady-state method.
The median estimates of the age of unfit banknotes are broadly similar across the three methods (Table 10). The median age estimates derived from the steady-state method are higher than those in the sample of unfit banknotes, particularly for $10 banknotes. The results are most similar between the steady-state method and the sample for $5 banknotes; however, the 2011 period coincides with a cleansing program for the $5, which as discussed previously, causes the steady-state method to have lower life predictions than would otherwise be the case. The median estimates for the age of unfit banknotes generated by the survival models are, on average, closer to the median sample results, and are especially close for the $20.
| Denomination | Traditional steady state(a) | Survival models | Unfit sample |
|---|---|---|---|
| $5 | 5.3 | 4.3 | 5.2 |
| $10 | 7.3 | 4.4 | 4.9 |
| $20 | 5.3 | 4.4 | 4.6 |
| $50 | 6.6 | 5.4 | 6.1 |
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Note: (a) Calculated based on the average hazard rates predicted over 2011 Sources: Author's calculations; RBA |
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The overall shape of the distribution of unfit banknotes across vintages predicted by the survival models is similar to the distribution in the sample (Figure 8).
7.2 Sampling Banknotes in Circulation
A second sample methodology used by the Reserve Bank is the commercial cash sampling (CCS) program. This program involves taking samples of unsorted banknotes from cash-in-transit (CIT) companies across the country. Although the purpose of this program is to assess the quality of circulating banknotes, it also provides an opportunity to examine the vintages of banknotes in circulation.[17]
Examining three sample periods (February in each of 2011, 2012 and 2013) shows that the median ages of banknotes in circulation from the CCS samples tend to be closer to those predicted by the survival models (Table 11). Again, the traditional steady-state method tends to imply higher median ages for banknotes on issue than predicted by the survival models and the CCS sample.
| Denomination | Traditional steady state(a) | Survival models | CCS sample | ||||||
|---|---|---|---|---|---|---|---|---|---|
| 2011 | 2012 | 2013 | 2011 | 2012 | 2013 | 2011 | 2012 | 2013 | |
| $5 | 5.7 | 5.9 | 6.8 | 5.5 | 6.0 | 6.7 | 4.8 | 5.2 | 5.9 |
| $10 | 4.8 | 5.9 | 7.2 | 4.6 | 5.3 | 6.6 | 4.4 | 5.0 | 6.6 |
| $20 | 5.4 | 5.9 | 6.4 | 5.3 | 5.9 | 6.3 | 4.3 | 5.0 | 5.7 |
| $50 | 6.7 | 7.2 | 7.8 | 5.5 | 6.1 | 6.5 | 5.1 | 5.6 | 6.1 |
|
Note: (a) Calculated based on the average hazard rates predicted over each year to February Sources: Author's calculations; RBA |
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Looking more closely at the 2013 sample, however, it appears that the survival models predict a larger number of early vintage banknotes in circulation than represented in the CCS sample, particularly for the $5 and $10 banknotes (Figure 9). Although the survival models take into account that some banknotes circulate actively and others are stored, each vintage is assumed to have the same propensity to be used in transactions. It is possible, however, that cleansing programs for the lower-value denominations have removed many of the early vintage banknotes out of active circulation and banknotes from these early vintages may be more likely to be stored if, for instance, they are of greater numismatic interest. Another contributing factor could be that retailers retain good quality low-value banknotes in their cash registers, whereas all high-value denominations are returned to the CITs for processing.
Footnotes
It is important to note that this measure is different to the median life of banknotes discussed in Section 6.3. [15]
The first two numbers of a banknote's serial number identify the year a banknote was manufactured. For more information on serial numbers, see the production section of the RBA's Banknotes microsite at <http://banknotes.rba.gov.au/production-and-distribution/production/>. [16]
It should be noted that with around two to three thousand banknotes collected for each denomination, the samples are small relative to the stock of banknotes on issue and that the samples can only be drawn from the pool of banknotes that actively circulate. [17]